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arXiv · 2610.35127

Deformations of the logarithmic tangent bundle of smooth projective surfaces

Sukmoon Huh·Min-Gyo Jeong
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Abstract

We study fixed-determinant deformations of the logarithmic tangent bundle associated with a smooth irreducible divisor on a smooth complex projective surface. We derive numerical criteria for the existence of positive-dimensional deformation families. Using the Enriques--Kodaira classification and Miyaoka-type inequalities, we classify the minimal surface pairs whose logarithmic tangent bundle is infinitesimally rigid. We also prove monotonicity under compatible blow-ups and compute local comparison formulas for resolutions of low-multiplicity ordinary singularities of the boundary.

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Sukmoon Huh, Min-Gyo Jeong. 2026-10-26. Deformations of the logarithmic tangent bundle of smooth projective surfaces. https://arxiv.org/abs/2610.35127

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